Properties

Label 1323.2.be
Level $1323$
Weight $2$
Character orbit 1323.be
Rep. character $\chi_{1323}(68,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $696$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 1056 744 312
Cusp forms 960 696 264
Eisenstein series 96 48 48

Trace form

\( 696q + 3q^{2} + 9q^{3} + 3q^{4} + 9q^{5} + 18q^{6} - 36q^{8} - 9q^{9} + O(q^{10}) \) \( 696q + 3q^{2} + 9q^{3} + 3q^{4} + 9q^{5} + 18q^{6} - 36q^{8} - 9q^{9} + 15q^{11} + 9q^{12} - 3q^{16} + 18q^{17} + 3q^{18} - 18q^{20} - 24q^{22} + 18q^{23} + 9q^{24} + 3q^{25} - 42q^{29} + 57q^{30} + 9q^{31} - 33q^{32} + 9q^{33} + 18q^{34} - 36q^{36} - 3q^{37} + 99q^{38} + 84q^{39} + 54q^{40} - 24q^{43} + 9q^{44} + 9q^{45} - 3q^{46} - 45q^{47} - 39q^{50} - 60q^{51} + 9q^{52} + 45q^{53} - 171q^{54} - 48q^{57} + 3q^{58} - 36q^{59} - 27q^{60} + 9q^{61} + 99q^{62} + 252q^{64} - 99q^{65} + 9q^{66} + 3q^{67} - 36q^{68} - 108q^{69} - 108q^{71} + 249q^{72} + 9q^{73} - 123q^{74} - 36q^{75} - 36q^{76} - 162q^{78} + 39q^{79} - 72q^{80} + 63q^{81} + 18q^{82} + 90q^{83} - 81q^{85} + 99q^{86} + 54q^{87} + 27q^{88} + 18q^{89} - 81q^{90} - 258q^{92} - 9q^{93} + 9q^{94} + 183q^{95} + 81q^{96} - 144q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)